| In the classical rough set, based on the upper or lower approximation operators, we can constructe topological space, In this paper, we discuss the properties of a kind of upper and lower approximation operators in concept lattice.we also obtain the conditions for constructing topological space with the upper and lower approximation operators.Firstly, in section 2, we give a brief introduction to the concept lattice and topological space, after that, we study the relation between lower set, upper set and upper bound, lower bound in order set. We also give the specific representation of their relation in lattice and the complete lattice.Secondly, in section 3, we give a brief introduction to the classical rough sets. We obtain some the conditions of constructing topological space based on the upper and lower approximation operators in concept lattice.Thirdly, we obtain some properties of topological space based on the upper and lower approximation operators in concept lattice:(1) If (U,T) is a topological space, then B=EXT(J(L))∪(?) is a base of (U,T),where J(L) is the set of irreducible elements of the concept lattice L.(2)If(U, T) is a topological space, then B=EXT(L) is a cover of U,and EXT(J(L)) is a reduction of the cover B.(3) If (U, T) is a topological space.Where U is a finite set, then this topological space has countable base,and the cover of every subset of U has a countable sub-coverage.(4) If (U,T) is a topological space, then for any x E U such that A={x} if and only if (U, T) is a Hausdorff space. |
